Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C4×D13 | C2 | semidirect |
| 3. C3×C42×C13 | C2 | semidirect |
| 4. C3×#6103 | C2 | semidirect |
| 5. C3×C4⋊Dic13 | C2 | semidirect |
| 6. C4×D52 | C3 | direct (N × H) |
| 12. C3×D52 | C4 | direct (N × H) |
| 15. C2×C4×D13 | C2×C3 | semidirect |
| 16. C42×C13 | C2×C3 | semidirect |
| 17. #6103 | C2×C3 | semidirect |
| 18. C4⋊Dic13 | C2×C3 | semidirect |
| 22. C2×C3×D13 | C2×C4 | semidirect |
| 24. C3×C4×C13 | C2×C4 | semidirect |
| 25. C3×C4×C13 | D4 | semidirect |
| 32. D52 | C3×C4 | direct (N × H) |
| 42. C2×D13 | C2×C3×C4 | semidirect |
| 44. C4×C13 | C2×C3×C4 | semidirect |
| 45. C4×C13 | C3×D4 | semidirect |
| 51. C3×C42 | D13 | semidirect |
| 52. C3×C13 | C4×D4 | semidirect |
| 69. C42 | C3×D13 | semidirect |
| 70. C13 | C3×C4×D4 | semidirect |
| 77. C3×C4 | C4×D13 | semidirect |
| 78. C3×C4 | D52 | direct (N × H) |
| 96. C4 | C3×C4×D13 | semidirect |
| 97. C4 | C3×D52 | direct (N × H) |
| 98. C3 | C4×D52 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D52 | 2 |
| C2×C3×C4×D13 | 2 |
| C3×C42×C13 | 2 |
| C3×#6103 | 2 |
| C3×C4⋊Dic13 | 2 |
| C4×D52 | 3 |
| C3×C4×D4 | 13 |